Basic properties
Modulus: | \(8016\) | |
Conductor: | \(8016\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(332\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bt
\(\chi_{8016}(5,\cdot)\) \(\chi_{8016}(53,\cdot)\) \(\chi_{8016}(101,\cdot)\) \(\chi_{8016}(125,\cdot)\) \(\chi_{8016}(149,\cdot)\) \(\chi_{8016}(197,\cdot)\) \(\chi_{8016}(245,\cdot)\) \(\chi_{8016}(269,\cdot)\) \(\chi_{8016}(389,\cdot)\) \(\chi_{8016}(413,\cdot)\) \(\chi_{8016}(437,\cdot)\) \(\chi_{8016}(485,\cdot)\) \(\chi_{8016}(581,\cdot)\) \(\chi_{8016}(605,\cdot)\) \(\chi_{8016}(773,\cdot)\) \(\chi_{8016}(797,\cdot)\) \(\chi_{8016}(821,\cdot)\) \(\chi_{8016}(845,\cdot)\) \(\chi_{8016}(869,\cdot)\) \(\chi_{8016}(917,\cdot)\) \(\chi_{8016}(941,\cdot)\) \(\chi_{8016}(1037,\cdot)\) \(\chi_{8016}(1061,\cdot)\) \(\chi_{8016}(1085,\cdot)\) \(\chi_{8016}(1133,\cdot)\) \(\chi_{8016}(1157,\cdot)\) \(\chi_{8016}(1229,\cdot)\) \(\chi_{8016}(1325,\cdot)\) \(\chi_{8016}(1349,\cdot)\) \(\chi_{8016}(1373,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{332})$ |
Fixed field: | Number field defined by a degree 332 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((1,i,-1,e\left(\frac{145}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 8016 }(149, a) \) | \(1\) | \(1\) | \(e\left(\frac{207}{332}\right)\) | \(e\left(\frac{95}{166}\right)\) | \(e\left(\frac{69}{332}\right)\) | \(e\left(\frac{239}{332}\right)\) | \(e\left(\frac{66}{83}\right)\) | \(e\left(\frac{137}{332}\right)\) | \(e\left(\frac{79}{166}\right)\) | \(e\left(\frac{41}{166}\right)\) | \(e\left(\frac{91}{332}\right)\) | \(e\left(\frac{51}{83}\right)\) |